25 nov 2010 · The aim of this thesis is to successfully forecast the future exchange rates of the 2 5 Example Calculations of Numerical Descriptive Methods
| Previous PDF | Next PDF |
[PDF] CHAPTER V FORECASTING EXCHANGE RATES One of the goals
Based on the information set used by the forecaster, there are two pure approaches to forecasting foreign exchange rates: (1) The fundamental approach (2) The technical approach The fundamental approach is based on a wide range of data regarded as fundamental economic variables that determine exchange rates
Exchange Rate Forecasting: Techniques and Applications
Exchange Rate Forecasting: Techniques and Applications Imad A Moosa Reader in Economics and Finance La Trobe University MACMILLAN Business
[PDF] Forecasting Exchange Rates - CORE
25 nov 2010 · The aim of this thesis is to successfully forecast the future exchange rates of the 2 5 Example Calculations of Numerical Descriptive Methods
[PDF] CHAPTER 8 EXCHANGE RATE FORECASTING
Cases in which accurate forecasts might not be profitable are illustrated The chapter reviews exchange rate forecasting methods with some specific examples
[PDF] Exchange Rate Forecasting - Stanford University
- Could reflect elements of both the pegged and floating process - Under the Exchange Rate Mechanism (ERM) of the European Monetary System, exchange
[PDF] method that calls itself java
[PDF] method that calls itself repeatedly
[PDF] methode apprendre a lire a 4 ans
[PDF] méthode de gauss
[PDF] methode facile pour apprendre la division
[PDF] méthode pour apprendre à compter cp
[PDF] méthode pour apprendre à lire à 3 ans
[PDF] methode pour apprendre l'hebreu
[PDF] méthode pour apprendre l'histoire géographie
[PDF] methode pour apprendre la division
[PDF] methode pour apprendre les divisions
[PDF] methode pour apprendre les divisions en ce2
[PDF] méthode rapport de stage droit
[PDF] methode simple pour apprendre la division
Forecasting Exchange Rates Ashley Rose Granvik Degree Thesis International Business 2010
BACHELOR'S DEGREE THESIS Arcada Polytechnic Degree Programme: International Business Identification number: 8253 Author: Ashley Rose Granvik Title: Forecasting Exchange Rates Supervisor (Arcada): Karis Badal Durbo Commissioned by: Abstract: The work of this thesis primarily revolves around the concept of forecasting the daily exchange rates of the European Euro valued in United States Dollars. Forecasting is a relatively important issue in busi ness operations, however it i s also one of the most problematic. With the uncertainty of the future, forecasts are difficult to assess. The aim of this thesis is to successfully forecast the future exchange rates of the European Euro in terms of United States Dollars for the month of May 2010, and determine whether the forecasting models properly work when applied to exchange rates, why or why not, and their measure of accuracy. The methodology of this thesis revolves extensively around quantitative research, largely incl uding a probability and forecasting approach. Throughout a period of three months, actual exchange rate values were collected and recorded to form a data set. The exchange rate data was then used in the application of a variety of mathematical forecasting models to forecast the daily exchange rates for a future, one-month period. Upon measuring the accuracy of the forecasts, the forecasted exchange rates contained very little error. Therefore, the forecasts are considered to be successful, and the hypothesis that exchange rates could be determined with the aid of a mathematical forecasting model is accepted. Though it is very difficult to consistently estimate exchange rates successfully, the work of this thesis shows there is always a greater probability of benefiting from a forecast. Keywords: Economics, Exchange Rates, Forec asting, Mathematic s, Quantitative Number of pages: 88 Language: English Date of acceptance: 25/11/2010
TABLE OF CONTENTS 1 INTRODUCTION.......................................................................111.1 Description and Motivation for Topic....................................................111.2 Aim of Research...................................................................................111.3 Hypotheses...........................................................................................111.4 Description of Methods.........................................................................121.5 Limitations............................................................................................121.6 Technical frame of reference................................................................122 DESCRIPTIVE MEASURES.....................................................142.1 Numerical Descriptive Methods............................................................142.2 Measures of Central Tendency............................................................142.2.1 Mean......................................................................................................................142.2.2 Median...................................................................................................................152.2.3 Mode......................................................................................................................152.3 Measures of Variability.........................................................................152.3.1 Range....................................................................................................................162.3.2 Variance.................................................................................................................162.3.3 Standard Deviation................................................................................................172.4 Simple Index Numbers.........................................................................182.5 Example Calculations of Numerical Descriptive Methods....................192.5.1 Data.......................................................................................................................192.5.2 Mean......................................................................................................................192.5.3 Median...................................................................................................................202.5.4 Mode......................................................................................................................202.5.5 Range....................................................................................................................202.5.6 Population Variance...............................................................................................202.5.9 Population Standard Deviation..............................................................................212.5.8 Sample Variance....................................................................................................212.5.10 Sample Standard Deviation.................................................................................222.5.8 Simple Index Numbers...........................................................................................223 BACKGROUND OF FORECASTING.......................................243.1 Forecasting Approaches.......................................................................243.1.1 Quantitative Forecasting........................................................................................243.1.2 Econometric Forecasting Models...........................................................................253.1.3 Time-series Forecasting Models............................................................................253.2.1 Types of Forecasts................................................................................................263.2.2 Time Horizons........................................................................................................273.3 Forecasting System..............................................................................273.4 Importance of Forecasting....................................................................28
4 FORECASTING MODELS........................................................294.1 Naive Approach....................................................................................294.2 Simple Moving Averages......................................................................294.3 Exponential Smoothing.........................................................................304.3.1 Smoothing Constant..............................................................................................304.4 Exponential Smoothing with Trend Adjustment....................................314.5 Linear Regression................................................................................324.6.1 Assumptions Underlying Linear Regression..........................................................334.6.2 The Standard Error of Estimate.............................................................................334.6.3 Correlation Analysis...............................................................................................345 MEASURING ERROR...............................................................365.1 Measures of Forecast Accuracy...........................................................365.2 Mean Absolute Deviation......................................................................365.3 Mean Squared Error.............................................................................365.4 Root Mean Square Error......................................................................375.5 Mean Absolute Percentage Error.........................................................376 EXCHANGE RATES.................................................................396.1 Background of Foreign Exchange Rates..............................................396.2 Forecasting Exchange Rates...............................................................396.2.1 Influencing Factors.................................................................................................396.2.2 Economical Forecasting Models............................................................................406.2.3 Time Horizons........................................................................................................426.3 Limitations............................................................................................427 DATA.........................................................................................448 CALCULATIONS FOR FORECASTING THE EXCHANGE RATES.........................................................................................468.1 Naive Approach....................................................................................468.2 Moving Average....................................................................................478.3 Exponential Smoothing.........................................................................488.4 Exponential Smoothing With Trend Adjustment...................................498.5 Linear Regression................................................................................519 CALCULATIONS FOR MEASURING ERROR.........................559.1 Mean Absolute Deviation......................................................................559.2 Mean Squared Error.............................................................................599.3 Root Mean Squared Error....................................................................639.4 Mean Absolute Percentage Error.........................................................6710 RESULTS................................................................................7211 CONCLUSION........................................................................74
BIBLIOGRAPHY..........................................................................76APPENDICES..............................................................................77Appendix 1..................................................................................................77Appendix 2..................................................................................................77Appendix 3..................................................................................................78Appendix 4..................................................................................................79Appendix 5..................................................................................................79Appendix 6..................................................................................................80Appendix 7..................................................................................................81Appendix 8..................................................................................................81Appendix 9..................................................................................................82Appendix 10................................................................................................83Appendix 11................................................................................................83Appendix 12................................................................................................84Appendix 13................................................................................................85Appendix 14................................................................................................85Appendix 15................................................................................................86Appendix 16................................................................................................87Appendix 17................................................................................................87
TABLES Table 1...........................................................................................................19 Table 2...........................................................................................................44 Table 3...........................................................................................................46 Table 4...........................................................................................................47 Table 5...........................................................................................................49 Table 6...........................................................................................................51 Table 7...........................................................................................................54 Table 8...........................................................................................................56 Table 9...........................................................................................................56 Table 10.........................................................................................................57 Table 11.........................................................................................................58 Table 12.........................................................................................................58 Table 13.........................................................................................................60 Table 14.........................................................................................................60 Table 15.........................................................................................................61 Table 16.........................................................................................................62 Table 17.........................................................................................................62 Table 18.........................................................................................................64 Table 19.........................................................................................................65 Table 20.........................................................................................................65 Table 21.........................................................................................................66 Table 22.........................................................................................................67 Table 23.........................................................................................................68 Table 24.........................................................................................................69 Table 25.........................................................................................................70 Table 26.........................................................................................................70 Table 27.........................................................................................................71
FORMULAS Formula 1. ......................................................................................................14Formula 2.......................................................................................................16Formula 3.......................................................................................................16Formula 4.......................................................................................................17Formula 5.......................................................................................................18Formula 6.......................................................................................................18Formula 7.......................................................................................................18Formula 8.......................................................................................................29Formula 9. .....................................................................................................29Formula 10.....................................................................................................30Formula 11.....................................................................................................31Formula 12.....................................................................................................31Formula 13.....................................................................................................31Formula 14.....................................................................................................32Formula 15.....................................................................................................32Formula 16.....................................................................................................32Formula 17.....................................................................................................33Formula 18.....................................................................................................34Formula 19.....................................................................................................36Formula 20.....................................................................................................37Formula 21.....................................................................................................37Formula 22.....................................................................................................38Formula 23.....................................................................................................40Formula 24.....................................................................................................41Formula 25.....................................................................................................42
ABBREVIATIONS• EUR/EURO: European Euro • FX: Foreign Exchange • MAD: Mean Absolute Deviation • MAPE: Mean Absolute Percent Error • MSE: Mean Squared Error • PPP: Purchasing Power Parity • RMSE: Root Mean Squared Error • U.S: United States • USD: United States Dollar
DEFINITIONS • Actual Data - Any number of values that have been historically recorded. • Data - A collection of organized information from which conclusions may be drawn. • Equation - Two mathematical models expressed as being equal to each other. • Expected Value - The average value that an experiment is expected to produce if it is repeated a large amount of times. • Forecasting - The science of predicting future events, which may involve taking historical data and projecting them into the future with the application of a mathematical model. • Formula - A systematical process of a mathematical model. • Model - A system of numbers and/or variables that represent a real-life situation. • Probability - The likelihood or chance that an event will occur. • Sample - A limited quantity of something that is intended to represent the whole. • Sample Size - The number of observations that is to be included within a defined sample. • Trend - A general direction of movement.
11 1 INTRODUCTION 1.1 Description and Motivation for Topic The work of this thesis primarily revolves around the concept of forecasting the daily exchange rates of the European Euro (EUR) valued in United States Dollars (USD). Throughout a period of three months, actual exchange rate values were collected and recorded to form a data set. The exchange rate data was then used in the application of a variety of forecasting models to forecast the daily exchange rates for a future, one-month period. As the month approached, the actual exchange rates were collected and recorded. Lastly, the actual exchange rates were compared with the forecasted exchange rates to form an analysis that measured the forecasting accuracy of the various models. The thesis has been largely motivated by an operations management course and a statistics course completed by the author. With a curiosity to perform a forecast upon completion of the operations management course, the thesis topic was developed instantaneously. 1.2 Aim of Research Forecasting is a relatively important issue in business operations, however it also happens to be one of the most problematic of issues. Because the future is always uncertain, forecasts are difficult to assess; yet they are rarely ever avoidable in effective business planning. The aim of this thesis is to successfully forecast the future exchange rates of the EUR in terms of USD for the month of May 2010. Furthermore, the author expects to determine whether the forecasting models properly work when applied to exchange rates, why or why not, and their measures of accuracy. 1.3 Hypotheses 1. Future exchange rates can be determined with the aid of a mathematical forecasting model. 2. Future exchange rates cannot be determined with the aid of a mathematical forecasting model.
12 1.4 Description of Methods The methodology of this thesis revolves extensively around quantitative research, and largely includes a probability and forecasting approach. The forecasting system that is implemented involves the determining of an appropriate sample size, a collection of the necessary data, the application of relevant forecasting models, and an analysis of the results. Additionally, a variety of mathematical models that are commonly used in forecasting are applied to the sample of collected exchange rate data. These models include a naive approach, a moving average, exponential smoothing, and linear regression. 1.5 Limitations It is evident that forecasting exchange rates is no simple task. Therefore, a variety of limitations are present within the work of this thesis. Foremost, there are approximately one hundred eighty-two currencies in existence throughout the world. The foreign exchange rate data that is used in this thesis only includes two currencies, which happen to be one of the most common pairs in currency trading. Due to the lack of randomness, a biased selection of variables exist; making it unknown whether or not the same results would be achieved when using a different, unbiased, pair of currencies. Furthermore, there are numerous forecasting models available, however, this thesis only includes models that are familiar to the author. Therefore, it is uncertain whether these models are actually efficient in forecasting exchange rates. Additionally, it is imperative to bear in mind that the forecasting models used in this thesis do not support the probability of natural disasters or political/economical factors occurring. Lastly, since exchange rates do not typically follow an identifiable trend, it is difficult to conclude whether or not the same results would be achieved at a different period of time. 1.6 Technical frame of reference A majority of the theories that this thesis is based upon have been referenced from four significant works of literature. Lind, Marchal, and Mason's "Statistical Techniques in Business & Economics" (2002) was a fundamental element in interpreting the theories of correlation, linear regression, indexes, and dispersion. Mendenhall, Reinmuth, and Beaver's "Statistics for Management and Economics" (1993) was essential in supporting the theories of the measures of central tendency, as
13 well as the measures of forecast accuracy. Heizer and Render's "Operations Management" (2004) was the core foundation for explaining the theory of forecasting. Lastly, Henderson's "Currency Strategy" (2002) and Rosenberg's "Exchange-Rate Determination" (2003) provided the framework for the context of exchange rates. Additional text was referenced from relevant internet sites that contained theories pertaining to forecasting and exchange rates.
14 2 DESCRIPTIVE MEASURES 2.1 Numerical Descriptive Methods "When presented with a set of quantitative data, most people have difficulty making any sense out of it" (Mendenhall, Reinmuth, & Beaver, 1993, p. 16). An efficient way of illustrating the significances of a data set is to present the data's numerical descriptive methods. Descriptive methods signify the first approach to organizing, summarizing, and presenting a set of data informatively. Descriptive methods are particularly useful in quickly gathering an initial description of data because they provide a generalization of the center and spread of the set of data. Numerical descriptive measures can be divided into two categories: measures of central tendency and measures of variability. The measures of central tendency identify the center of the data, while the measures of variability describe how closely the data values are located to the data's center. (Mendenhall, Reinmuth, & Beaver, 1993),(Lind, Marchal, & Mason, 2002) 2.2 Measures of Central Tendency A measure of central tendency is a descriptive method that is used to locate the center of distribution of a set of data. Measures of central tendency summarize the data by determining a single numerical value to represent the data set. There are numerous measures of central tendency, and presented below are a few of the most common. (Mendenhall, Reinmuth, & Beaver, 1993), (Lind, Marchal, & Mason, 2002) 2.2.1 Mean The arithmetic mean, also referred to as simply the mean, is a very useful and quite common measure of central tendency. The mean is used in mathematics to measure the average of a set of data. The arithmetic mean of a data set can be expressed as the following formula: €
x = x i i=1 n n (1)15 Where €
x = the symbol used to denote the mean n = the number of measurements in the sample, and € x i i=1 n= the summation of the data values. The mean is a delicate measure of central tendency, however, as it is easily influenced by extreme data values. Therefore, it is important to note that the arithmetic mean may not always be accurately representative of the data set. (Mendenhall, Reinmuth, & Beaver, 1993) 2.2.2 Median The median is a second example of a measure of central tendency. When the data is arranged in order of ascending value, the median is the value that divides the data into two equal parts. The median can easily be identified with an odd-quantity set of data, however when there is an even-quantity set of data the median must be found by calculating the average of the two middle values. (Mendenhall, Reinmuth, & Beaver, 1993) 2.2.3 Mode A third example that can also be used as a measure of central tendency is the mode. The mode is found by identifying the data value that has the greatest frequency of occurrence. Though the mode is not used as often as the mean or median, it can be useful in cases where the frequency is considered to be a significant part of the evaluation. (Mendenhall, Reinmuth, & Beaver, 1993) 2.3 Measures of Variability Once the center of distribution for a data set has been identified, the next part of the process is to provide a measure of the variability. Variation is a very important property of data, as its measure is necessary in visualizing the distribution of frequencies.
16 Dispersion is a term used in statistics to describe the variation within a data set. While the mean or median identify the average value for a set of data, the measure of dispersion determines the distance from the data's average to the minimum and maximum values. Dispersion allows the forecaster to determine whether the average is, or is not, representative of the data according to how close the data values are situated to the measure of central tendency. A large measure of dispersion indicates a wide variation in data values, while a small measure of dispersion indicates little variation. Therefore, a small dispersion measure would indicate that the mean or median is representative of the data. (Mendenhall, Reinmuth, & Beaver, 1993), (Lind, Marchal, & Mason, 2002) 2.3.1 Range The simplest way to measure the dispersion of a data set is by using the range. The range can be determined by calculating the difference between the highest and lowest values within a data set. The following exemplifies this as an equation: Range = highest value - lowest value (2) (Lind, Marchal, & Mason, 2002), (Mendenhall, Reinmuth, & Beaver, 1993) 2.3.2 Variance The variance can be defined as the arithmetic mean of the squared deviations from the mean of a set of data, in which the deviation is the difference between the mean of a data set and its data values. The variance is a measure that is used to describe a data set's variation from the mean. By squaring the deviations, it becomes impossible for the variance to be negative in value. Additionally, the variance will only be zero if the values of the data set are equivalent. Population Variance The formula for the population variance is: €
2 x i 2 i=1 n n (3) Where € 2 = the symbol used to denote the population variance n = the number of items in the sample17 €
i=1 n = the summation of n items, and € x i 2= the squared value of the mean subtracted from an item in the sample. Sample Variance The formula for the sample variance is: €
s 2 x i -x 2 i=1 n n-1 (4) Where € s 2 = the symbol used to denote the sample variance n = the number of items in the sample € i=1 n = the summation of n items, and € x i -x 2= the squared value of the mean subtracted from an item in the sample. Similar to the other measures of variability and the measures of central tendency, the variance is a descriptive method that can be used to compare the variability in two or more sets of data. It is often difficult, however, to interpret the significance of the variance in one set of data due to its squared value. (Lind, Marchal, & Mason, 2002) 2.3.3 Standard Deviation A simpler way to interpret the variance is with the measure of the standard deviation. The standard deviation is defined as the square root of the variance. By un-squaring the variance, the value is transformed into the same unit of measurement as the set of data. In the previous section we mentioned it is impossible for the variance to be negative in value. This is essential for the standard deviation formula to work, as the square root does not work with negative numbers.
18 Population Standard Deviation The formula for the population standard deviation is: €
x i 2 i=1 n n (5) Where €= the symbol used to denote the population standard deviation n = the number of items in the sample €
i=1 n = the summation of n items, and € x i 2= the squared value of the mean subtracted from an item in the sample. Sample Standard Deviation The formula for the sample standard deviation is: €
s x i -x 2 i=1 n n-1 (6) Where € s= the symbol used to denote the sample standard deviation n = the number of items in the sample €
i=1 n = the summation of n items, and € x i -x 2= the squared value of the mean subtracted from an item in the sample. (Lind, Marchal, & Mason, 2002) 2.4 Simple Index Numbers A simple index number, also known as just an index number, refers to a number for a defined period of time that expresses a change in value relative to a base period. The change in value of the indexed number is for a single variable and can be represented by the following equation: €
P= p t p 0 ∗100 (7)19 Where €
p t = the amount at any given period, and € p 0= the base-period amount. The use of index numbers conveniently expresses the change within a diverse set of data by showing the ratios of one time period to another. Additionally, by converting the data into an index, it is easier to observe any visible trends within the data set. (Lind, Marchal, & Mason, 2002) 2.5 Example Calculations of Numerical Descriptive Methods In addition to individually explaining each of the basic numerical descriptive methods, a simple example of each method is solved below to demonstrate the application of these formulas. 2.5.1 Data The following table provides a fictive set of data to be used in solving the examples. Table 1. Sample data used for solving the numerical descriptive methods. Sample Data X 11 25 38 25 6 2.5.2 Mean €
x = x i i=1 5 5 x = (x5 + x4 + x3 + x2 + x1) / 5 € x = (6 + 25 + 38 + 25 + 11) / 5 ! x = x i i=1 n n20 €
x = 105 / 5 € x= 21 2.5.3 Median Since there is no equation for finding the median, the median is found by simply identifying the number in the sample that is located directly in the middle. In this case the median is 38. 2.5.4 Mode Since there is no equation for finding the mode, the mode is found by simply identifying the number in the sample that has the greatest frequency of occurrence. In this case the mode is 25. 2.5.5 Range Range = highest value - lowest value Before the range can be calculated, the data must first be arranged in order from smallest to largest. Data(smallest to largest) = 38, 25, 25, 11, 6 The formula for finding the range is then calculated as follows: Range = x5 - x1 Range = 38 - 6 Range = 32 2.5.6 Population Variance €
2 x i -x i i=1 5 5 i=1 5 2 5 2 x i x 5 +x 4 +x 3 +x 2 +x 1 5 2 i=1 5 5 2 x i 2 i=1 n n21 €
2 x i6+25+38+25+11
5 2 i=1 5 5 2 x i 1055 2 i=1 5 5 2 x i -21 2 i=1 5 5 2 = [(x5 - 21)2 + (x4 - 21)2 + (x3 - 21)2 + (x2 - 21)2 + (x1 - 21)2] / 5 € 2 = [(6 - 21)2 + (25 - 21)2 + (38 - 21)2 + (25 - 21)2 + (11 - 21)2] / 5 € 2 = [(-15)2 + (4)2 + (17)2 + (4)2 + (-10)2] / 5 € 2 = (225 + 16 + 289 + 16 + 100) / 5 € 2 = 646 / 5 € 2 = 129.2 2.5.9 Population Standard Deviation € 2
σ=129.2
= 11.367 2.5.8 Sample Variance € s 2 x i -x 2 i=1 n n-1 s 2 x i -x i i=1 5 5 i=1 5 2 5-1 x i 2 i=1 n n22 €
s 2 x i x 5 +x 4 +x 3 +x 2 +x 1 5 2 i=1 5 4 s 2 x i6+25+38+25+11
5 2 i=1 5 4 s 2 x i 1055 2 i=1 5 4 s 2 x i -21 2 i=1 5 4 s 2 = [(x5 - 21)2 + (x4 - 21)2 + (x3 - 21)2 + (x2 - 21)2 + (x1 - 21)2] / 4 € s 2 = [(6 - 21)2 + (25 - 21)2 + (38 - 21)2 + (25 - 21)2 + (11 - 21)2] / 4 € s 2 = [(-15)2 + (4)2 + (17)2 + (4)2 + (-10)2] / 4 € s 2 = (225 + 16 + 289 + 16 + 100) / 4 € s 2 = 646 / 4 € s 2 = 161.5 2.5.10 Sample Standard Deviation € s x i -x 2 i=1 n n-1 s s 2 s =161.5 s = 12.708 2.5.8 Simple Index Numbers P1 = (P1 / P1) * 100 ! P= p t p 0 "100
23 P1 = (11 / 11) * 100 P1 = 1 * 100 P1 = 100 P2 = (P2 / P1) * 100 P2 = (25 / 11) * 100 P2 = 2.272 * 100 P2 = 227.2 P3 = (P3 / P1) * 100 P3 = (38 / 11) * 100 P3 = 3.454 * 100 P3 = 345.4 P4 = (P4 / P1) * 100 P4 = (25 / 11) * 100 P4 = 2.272 * 100 P4 = 227.2 P5 = (P5 / P1) * 100 P5 = (6 / 11) * 100 P5 = 0.545 * 100 P5 = 54.5
24 3 BACKGROUND OF FORECASTING Forecasting is best described as the art and science of predicting a future event. It is the estimating of a future outcome of a random process. One of the main assumptions of forecasting is that the results achieved from the random process will provide accurate and reliable evidence of the future. However, limits do exist in what can be expected from a forecast. Though a forecast can provide a great amount of insight, it is rarely ever perfect. There are numerous unpredictable circumstances that can affect the actual outcome of a forecast. Nevertheless, businesses cannot afford to avoid the process of forecasting, as effective planning in both the short and long run often depend greatly on a forecast. (Heizer & Render, 2004), (Mendenhall, Reinmuth, & Beaver, 1993) 3.1 Forecasting Approaches There are two distinct approaches to making a forecast. One of the approaches, known as quantitative forecasting, is an arithmetical method and involves the implementation of a mathematical model to a set of data. It typically relies on historical data and does not include emotional or intuitional factors, like qualitative forecasting. Qualitative models are intended for situations where essential historical data is not available to the forecaster. (Heizer & Render, 2004), (Armstrong, 2001), (Mendenhall, Reinmuth, & Beaver, 1993) 3.1.1 Quantitative Forecasting Quantitative forecasting largely involves the use of historical data, which is projected into the future with the use of one ore more mathematical models. It may, however, in some cases also be a subjective or intuitive prediction based on qualitative forecasting, which focuses on subjective inputs that have been obtained from various sources like historical analogies or personal judgment. In such cases, quantitative forecasting becomes a combination of these two approaches and uses a mathematical model that is adjusted by the forecaster's intuition. Two subcategories of quantitative forecasting are time-series models and econometric models. The main difference between these two types of models is that while
25 econometric models include the use of supporting variables, time series models do not. (Heizer & Render, 2004) 3.1.2 Econometric Forecasting Models An econometric model can be defined as one or more equations that demonstrate the relationship amongst a variety of variables. The variables used in econometric forecasting are often a combination of a time series variable and any number of economic variables. An econometric model consists of one dependent variable and any number of independent variables. Econometric models are probabilistic models, meaning that they are calculated by estimating the probability that the dependent variable will reoccur based on the impact of the independent variables. While econometric models forecast by relating independent variables to a dependent variable, time series models forecast based on a dependent variable's history. (Mendenhall, Reinmuth, & Beaver, 1993) 3.1.3 Time-series Forecasting Models "Time-series models predict on the assumption that the future is a function of the past" (Heizer & Render, 2004, p. 107). Since time is often an important factor in decision-making, time-series forecasts were developed to utilize time in the foundation of the forecast. Therefore, time-series forecasts are based on a sequence of historical data points that are measured over any length of time, including daily, monthly or yearly. When a variable is measured over time, it allows for the visibility of possible trends. Once a trend has been identified, the most recent data is projected into the future according to the movement of the identified trend. The analyses of time series forecasts are largely influential, and often essential, to the formulating of future estimations, predictions, and many other major decisions that pertain to long-term planning. A few examples of the time-series models that have been implemented in the forecasting of this thesis include: naive approach, moving average, exponential smoothing, and trend projection. (Mendenhall, Reinmuth, & Beaver, 1993), (Lind, Marchal, & Mason, 2002), (Heizer & Render, 2004), (Shim, 2000)
26 3.2 Choosing a Forecasting Model Though there are many forecasting methods, there is no such thing as one superior method for use in all forecasting scenarios. "What works best in one firm under one set of conditions may be a complete disaster in another organization; or even in a different department of the same firm" (Heizer & Render, 2004, p. 104). Additionally, though it is relatively simple to apply many of the widely used methods, using a more complex forecasting model may improve the accuracy of the forecast. Nevertheless, these more complex methods often involve a meticulous data collection procedure and/or the application of a computer program, which can become quite costly. One of the most important parts of forecasting is being able to properly match a forecasting model to the data that is being forecasted. It is the responsibility of the forecaster to select a forecasting model that makes best use of the data that is available and fits within the forecaster's time and budget. Choosing a model is often intuitive and becomes recognizable to the forecaster through literary knowledge and experience from trial and error. During the process of selecting an appropriate forecasting model, the forecaster must review an assortment of criteria as part of the decision-making. The criterion includes the various types of forecasts and the time horizons of the forecasting period. (Heizer & Render, 2004) 3.2.1 Types of Forecasts The type of forecast depends on how the forecaster intends to use the information that is received through the forecasting of the data. There are three main types of forecasts that are commonly used in the planning of the future: 1. Economic forecasts: These types of forecasts address the business cycle. 2. Technological forecasts: These are concerned with the rate of technological progress. 3. Demand forecasts: Project the demand for a company's products or services. (Heizer & Render, 2004)
27 3.2.2 Time Horizons Another consideration when selecting a forecasting model is the time horizon for the forecasting period. Once the use of the forecast has been determined, the forecast is categorized by its time horizon. "Some models are more accurate for short-term time horizons and others are more reliable for long-term horizons" (Mendenhall, Reinmuth, & Beaver, 1993, p. 667). There are three kinds of time horizons: 1. Short-ranged forecasts: May have a time span of up to one year but are normally less than three months. 2. Medium-ranged forecasts: Generally span from three months to three years. 3. Long-ranged forecasts: Any length of time lasting three years or longer. With the constant change in demand patterns, long-term forecasts are normally used as a planning model for product lines and capital investment decisions, while short-term forecasts usually involve forecasting sales, price changes, and customer demand. (Mendenhall, Reinmuth, & Beaver, 1993) 3.3 Forecasting System The forecasting system is an exemplary guide for successfully completing a forecast. There are seven steps that form the forecasting system, and together they present a systematic way of initiating, designing, and implementing a forecasting project. The steps of the forecasting system have been applied throughout the forecasting within this thesis. The seven steps that form the forecasting system are: 1. Determine the use of the forecast. 2. Select the items to be forecasted. 3. Determine the time horizon of the forecast. 4. Select the forecasting model(s). 5. Gather the data needed to make the forecast. 6. Make the forecast. 7. Validate and implement the results. (Heizer & Render, 2004)
28 3.4 Importance of Forecasting Forecasting plays an important role in the success of many companies around the world. Inventory must be ordered without confidence of what sales will be, new equipment must be purchased with uncertainty of the final products' demand, and investments are commonly made without knowing what profits will be. Thus, it is important for forecasters to consistently make estimates of what will happen in the future. The projection of a good estimate is the core purpose of forecasting, as it is essential to efficient service and manufacturing operations. "A forecast is the only estimate of demand until actual demand becomes known" (Heizer & Render, 2004, p. 105). Therefore, effective planning in both the short and long run depends on forecasts, making it the drive behind many critical decisions. Due to the uncertainty of what the future may hold, it is very unlikely for a forecast to be completely accurate. Oftentimes, the further a forecast is projected into the future, the more apprehensive its outcome becomes. A majority of the results produced by a forecast are in some way influenced by one or more unexpected factors. A forecast, long or short-term, is rarely able to offset the effects of each and every possible influencing factor. Still, forecasting is often inevitable due to the probability of benefitting from the forecast, compared to not forecasting at all. It is important to consider forecasting as a practice that can consistently be perfected. As the forecaster gains experience, they become more capable of adjusting their methods according to changes within the forecast's environment. It is possible for even the worst forecasters to occasionally produce good forecasts, while even the best forecasters sometimes miss completely. (Heizer & Render, 2004), (Mendenhall, Reinmuth, & Beaver, 1993)
29 4 FORECASTING MODELS 4.1 Naive Approach The naive approach is the simplest way to make a forecast because there are no actual calculations involved in its determination. The approach is to assume that the demand in the next period will be the same as the demand in the most recent period. €
F t =A t-1 (8) Where € F t = the new forecast, and € A t-1= the previous period's actual value. (Heizer & Render, 2004), (Shim, 2000) 4.2 Simple Moving Averages A simple moving average, also referred to as moving average, is an approach that bases its forecast on an average of a fixed number of previous cycles within a data set. As time moves forward, the earliest data is excluded from the average to include the most recent cycle's actual data, creating a continuous inflow of current data and smoothes fluctuations. Therefore, by following this process, any irregular variations that may be present in the set of data are eliminated. This allows for any visible long-term trends within the set of data to be presented. The formula for a simple moving average is: €
F t A i i=1 n n (9) Where € F t = the new forecast n = the number of previous periods in the sample, and € A i i=1 n= the summation of the actual values for the previous n periods. Moving averages are useful when the forecaster can assume that the data will move steadily with time. When the data exhibits extreme, random movement a moving
30 average forecasting model is likely to provide inaccurate results. (Lind, Marchal, & Mason, 2002), (Heizer & Render, 2004), (Shim, 2000), (Mendenhall, Reinmuth, & Beaver, 1993) 4.3 Exponential Smoothing An exponential smoothing model can be described as a combination of a naive approach and a moving-average model, with an added smoothing constant. Exponential smoothing is used to reveal possible trends and seasonal and cyclic effects within a set of data. Similar to the other time-series models, exponential smoothing assumes that past trends and cycles will continue into the future. Though the exponential smoothing formula forecasts by extending these patterns, it involves very little record keeping and only uses one period of previous data. Naturally, a pattern does not always occur exactly the same as it did previously. Thus, a smoothing constant is included to reduce the random fluctuations that may exist within a pattern. The formula for exponential smoothing is as follows: €
F t =F t-1 +αA t-1 -F t-1 (10) Where € F t = the new forecast € F t-1 A t-1= the previous period's actual value. (Mendenhall, Reinmuth, & Beaver, 1993), (Heizer & Render, 2004), (Shim, 2000) 4.3.1 Smoothing Constant The symbol α, read as alpha, is used to represent a smoothing constant. A smoothing constant is a number that is used as a weight in forecasting to make adjustments to the previous forecast's error. The smoothing constant may range between 0 and 1 and is chosen by the forecaster. Deciding on the value of a smoothing constant for a set of data is no simple task. No formula exists for finding the best value. Thus, the smoothing constant is often found through trial and error. A high smoothing constant is used to give more weight to recent data while a low smoothing constant gives more weight to past data. When the smoothing constant is 1 the forecast relies solely on the
31 most recent data period and assumes that the new forecast is equal to the previous period's actual value, making it identical to a naive approach. A second smoothing constant, β, is used in addition to α when forecasting with trend adjustment. Pronounced as beta, this second smoothing constant is used to weight a measure of trend before it is added to an exponentially smoothed forecast to develop a forecast that accounts for trend. Similar to α, the value of β is chosen by the forecaster and must be a number that ranges between 0 and 1. Choosing a proper value for both smoothing constants is crucial and can often make the difference between an accurate forecast and an inaccurate forecast. (Mendenhall, Reinmuth, & Beaver, 1993), (Heizer & Render, 2004) 4.4 Exponential Smoothing with Trend Adjustment Exponential smoothing with trend adjustment is a modified exponential smoothing model that is able to respond to trends. In a simple exponential smoothing model, a lag between the forecast and actual amount is often present. A trend-adjusted exponential smoothing model is applied to reduce any lag and improve the forecast. The formula for exponential smoothing with trend adjustment is: €
FIT t =F t +T t(11) Where FIT = the abbreviation for forecasting with trend F = the exponentially smoothed forecast, and T = the exponentially smoothed trend. The exponentially smoothed forecast and trend can be found by the following formulas: €
F t =αA t-1 +1-α F t-1 +T t-1 (12) € T t =βF t -F t-1 +1-β T t-1 (13) Where € F t A t-1 = the previous period's actual value € F t-1 = the previous period's forecast32 €
T t-1 = the previous period's trend € T t y =a+bx (14) Where € y= the predicted value of the y variable for a selected value of x a = the y-intercept b = the slope of the line, and x = any value of the independent variable. The y-intercept and the slope of the linear regression model can be calculated using the following formulas: €
b= x i y i i=1quotesdbs_dbs14.pdfusesText_20